Understanding Recursion and Iteration

What is a recursive sequence?

• A sequence where each term is determined by one or more previous terms

• A sequence where each term is the sum of all previous terms

• A sequence where each term is independent of the others

• A sequence where each term is a random number

How do you find the nth term in an arithmetic sequence using a recursive formula?

• By dividing the previous term by the common ratio

• By subtracting the common difference from the previous term

• By adding the common difference to the previous term

• By multiplying the previous term by the common ratio

In a recursive sequence, why is it important to know the first term?

• It is necessary to calculate subsequent terms

• It helps in determining the common ratio

• It is used to find the sum of the sequence

• It allows for the sequence to be finite

What is the common ratio in a geometric sequence?

• The difference between consecutive terms

• The sum of the first and last terms

• The factor by which each term is multiplied to get the next term

• The average of all terms in the sequence

How do you recognize a geometric sequence?

• By identifying a constant product of terms

• By identifying a constant sum of terms

• By identifying a constant ratio between terms

• By identifying a constant difference between terms

If the third term of an arithmetic sequence is 6 and the common difference is 5, what is the first term?

• 6

• 11

• -4

• 1

What does iteration involve in the context of sequences?

• Multiplying each term by a constant value

• Adding a constant value to each term

• Composing a function onto itself repeatedly

• Subtracting a constant value from each term

What is the process of finding the second iterate in iteration?

• Adding the initial value to the function

• Multiplying the initial value by the function

• Composing the function with itself using the initial value

• Subtracting the initial value from the function

What is the result of the first iterate of the function f(x) = 3x - 1 when x_0 = 5?

• 14

• 16

• 15

• 17

In iteration, what is the third iterate of the function f(x) = 3x - 1 starting with x_0 = 5?

• 41

• 5

• 122

• 14